This study introduces a resource allocation framework for integrated satellite-terrestrial networks to address these challenges. The framework leverages local cache pool deployments and non-orthogonal multiple access (NOMA) to reduce time delays and improve energy efficiency. Our proposed approach utilizes a multi-agent enabled deep deterministic policy gradient algorithm (MADDPG) to optimize user association, cache design, and transmission power control, resulting in enhanced energy efficiency. The approach comprises two phases: User Association and Power Control, where users are treated as agents, and Cache Optimization, where the satellite (Bs) is considered the agent. Through extensive simulations, we demonstrate that our approach surpasses conventional single-agent deep reinforcement learning algorithms in addressing cache design and resource allocation challenges in integrated terrestrial-satellite networks. Specifically, our proposed approach achieves significantly higher energy efficiency and reduced time delays compared to existing methods.